Home
Class 11
MATHS
P is a point on the hyperbola (x^(2))/(a...

P is a point on the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`, and N is the foot of the perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transverse axis at T. If O is the centre of the hyperbola, then OT.ON is equal to

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

Ifthe normal at P to the rectangular hyperbola x^2-y^2=4 meets the axes in G and g and C is the centre of the hyperbola, then

The slope of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( x_(1),y_(1)) is-

Normal to a rectangular hyperbola at P meets the transverse axis at N. If foci of hyperbola are S and S', then find the value of (SN)/(SP).

Let P b any point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 whose ordinate is PN. AA′ is its transverse axis. If the point Q divides AP in the ratio a^(2):b^(2) , then NQ is?

The locus of the foot of the perpendicular from the center of the hyperbola x y=1 on a variable tangent is

Let P(4,3) be a point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 . If the normal at P intersects the x-axis at (16,0), then the eccentriclty of the hyperbola is

Find the points on the hyperbola 2x^(2)-3y^(2)=6 at which the slop of the tangent line is (-1)

Let P(6,3) be a point on the hyperbola parabola x^2/a^2-y^2/b^2=1 If the normal at the point intersects the x-axis at (9,0), then the eccentricity of the hyperbola is

The length of the transverse axis of the hyperbola 9y^(2) - 4x^(2) = 36 is -

If P Q is a double ordinate of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 such that O P Q is an equilateral triangle, O being the center of the hyperbola, then find the range of the eccentricity e of the hyperbola.

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. On which curve does the perpendicular tangents drawn to the hyperbola ...

    Text Solution

    |

  2. The minimum area of the triangle formed by the tangent to (x^2)/(a^2)+...

    Text Solution

    |

  3. P is a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1, and N...

    Text Solution

    |

  4. If P(x ,y) is any point on the ellipse 16 x^2+25 y^2=400 and f1=(3,...

    Text Solution

    |

  5. Find the equation of the hyperbola whose foci are (8,3)a n d(0,3) and ...

    Text Solution

    |

  6. The number of values of c such that the straight line y=4x+c touches t...

    Text Solution

    |

  7. Find the equations of tangents to the curve 4x^(2)-9y^(2)=1 which are ...

    Text Solution

    |

  8. Find the value of m for which y=mx+6 is a tangent to the hyperbola (x^...

    Text Solution

    |

  9. If a hyperbola passes through the foci of the ellipse (x^2)/(25)+(y^2)...

    Text Solution

    |

  10. One the x-y plane, the eccentricity of an ellipse is fixed (in size a...

    Text Solution

    |

  11. Find the equation of tangent to the conic x^2-y^2-8x+2y+11=0 at (2,1).

    Text Solution

    |

  12. The equation of one directrix of a hyperbola is 2x+y=1, the correspond...

    Text Solution

    |

  13. The distance of a point on the ellipse (x^2)/6+(y^2)/2=1 from the cent...

    Text Solution

    |

  14. A hyperbola having the transverse axis of length 2sintheta is confocal...

    Text Solution

    |

  15. If it is posssible to draw the tangent to the hyperbola (x^(2))/(a^(2)...

    Text Solution

    |

  16. The set of values of m for which it is possible to draw the chord y=sq...

    Text Solution

    |

  17. Find the equations of the tangents to the hyperbola x^(2)-9y^(2)=9 tha...

    Text Solution

    |

  18. Let a and b be nonzero real numbers. Then the equation (a x^2+b y^2+c)...

    Text Solution

    |

  19. x^2/(r^2-r-6)+y^2/(r^2-6r+5)=1 will represent ellipse if r lies in the...

    Text Solution

    |

  20. Find the equations to the common tangents to the two hyperbolas (x^2)/...

    Text Solution

    |